Michael A. Salinger

Vertical Mergers and Market Foreclosure

yThe model in this paper illustrates three effects of vertical mergers when both stages are oligopolistic and vertically integrated and unintegrated producers coexist. First, the merging firm increases its final good output. Second, the resulting backward shift in the residual demand curve facing unintegrated final good producers ylowers their demand for the intermediate good. Third, the merged firm withdraws from the intermediate good market. The increased concentration pushes the intermediate good price upward. Which effect dominates depends on market structure. Under some conditions, a vertical merger causes the price of the final good to increase.

Zipf plots and the size distribution of firms

We use a Zipf plot to demonstrate that the upper tail of the size distribution of firms is too thin relative to the log normal rather than too fat, as had previously been believed.

Tobin's q, Unionization, and the Concentration-Profits Relationship

This article uses Tobins q, the ratio of the market value of a firm to the replacement value of its physical assets, to measure monopoly power and to examine the relationship between market structure and profitability. Tobins q is a better measure of monopoly profits than indices of single-period profitability because it measures long-run monopoly power. In addition, it is subject to less measurement error and it contains an adjustment for risk. The relationship between q and long-run monopoly power is established. Provided that all inputs are supplied competitively, q should be highly sensitive to even small amounts of monopoly power. Since the level of q is generally not high in the American economy, the result suggests either that monopoly power is absent or that unions manage to capture monopoly rents. Empirical tests of the relationship between Tobins q and measures of market structure and unionization provide evidence that unions do capture most monopoly rents.

Standard Errors in Event Studies

Even if true abnormal returns are uncorrelated, estimated abnormal returns are not. This paper presents a simple formula for the variance of estimated cumulative abnormal returns. Both returns and dummy variable procedures for estimating the standard error correctly, taking account of both intertemporal and contemporaneous correlation of estimated residuals, are discussed. They are then applied to an event study of post-merger performance. It is shown that ignoring either the intertemporal or contemporaneous correlation of residuals can result in significant underestimates of standard errors.

Power Law Scaling for a System of Interacting Units with Complex Internal Structure

We study the dynamics of a system composed of interacting units each with a complex internal structure comprising many subunits and treat the case in which each subunit grows in a multiplicative manner. We propose a model for such systems in which the interaction among the units is treated in a mean field approximation and the interaction among subunits is nonlinear. We test the model and find agreement between our predictions and empirical results based on a large economics database spanning 20 years. [S0031-9007(98)05355-1]

Anomalous fluctuations in the dynamics of complex systems: from DNA and physiology to econophysics

We discuss examples of complex systems composed of many interacting subsystems. We focus on those systems displaying nontrivial long-range correlations. These include the one-dimensional sequence of base pairs in DNA, the sequence of flight times of the large seabird Wandering Albatross, and the annual fluctuations in the growth rate of business firms. We review formal analogies in the models that describe the observed long-range correlations, and conclude by discussing the possibility that behavior of large numbers of humans (as measured, e.g., by economic indices) might conform to analogs of the scaling laws that have proved useful in describing systems composed of large numbers of inanimate objects.

SCALING BEHAVIOR IN ECONOMICS : THE PROBLEM OF QUANTIFYING COMPANY GROWTH

Inspired by work of both Widom and Mandelbrot, we analyze the Computstat database comprising all publicly traded United States manufacturing companies in the years 1974–1993. We find that the distribution of company size remains stable for the 20 years we study, i.e., the mean value and standard deviation remain approximately constant. We study the distribution of sizes of the “new” companies in each year and find it to be well approximated by a log- normal. We find (i) the distribution of the logarithm of the growth rates, for a fixed growth period of T years, and for companies with approximately the same size S displays an exponential “tent-shaped” form rather than the bell-shaped Gaussian, one would expect for a log-normal distribution, and (ii) the fluctuations in the growth rates — measured by the width of this distribution σT — decrease with company size and increase with time T. We find that for annual growth rates (T = 1), σT ∼ S−β, and that the exponent β takes the same value, within the error bars, for several measures of the size of a company. In particular, we obtain β = 0.20 ± 0.03 for sales, β = 0.18 ± 0.03 for number of employees, β = 0.18±0.03 for assets, β = 0.18 ± 0.03 for cost of goods sold, and β = 0.20 ± 0.03 for propert, plant, and equipment. We propose models that may lead to some insight into these phenomena. First, we study a model in which the growth rate of a company is affected by a tendency to retain an “optimal” size. That model leads to an exponential distribution of the logarithm of growth rate in agreement with the empirical results. Then, we study a hierarchical tree-like model of a company that enables us to relate β to parameters of a company structure. We find that β = −1n Π/1nz, where z defines the mean branching ratio of the hierarchical tree and Π is the probability that the lower levels follow the policy of higher levels in the hierarchy. We also study the output distribution of growth rates of this hierarchical model. We find that the distribution is consistent with the exponential form found empirically. We also discuss the time dependence of the shape of the distribution of the growth rates.

Stock market margin requirements and volatility: Implications for regulation of stock index futures

This article reexamines the evidence on the relationship between stock market margin buying and volatility, and discusses the implications for the regulation of futures markets margin requirements. Post-war data provide no evidence of a link between the initial margin requirements set by the Federal Reserve and stock market volatility. Over the entire period in which the Federal Reserve has set margin requirements (1934-present), there is a correlation between margin requirements and margin debt on the one hand and volatility on the other. However, margin debt is not primarily associated with downside volatility and margin requirements are not primarily associated with upside volatility, as would be expected if margin buying were the cause of the volatility. Thus, the experience with stock market margin requirements provides no support for regulating futures markets margins in order to curb volatility. While this evidence does not rule out the possibility that margin buying contributed to the speculative boom of the 1920s and the 1929 crash, margin debt represented a much greater fraction of the 1929 stock market than have stock market futures in the 1980s. Even taking the experience of the 1920s into account, therefore, there is still no justification for regulating futures margins in order to curb volatility.

Can statistical physics contribute to the science of economics

In recent years, a breakthrough in statistical physics has occurred. Simply put, statistical physicists have determined that physical systems which consist of a large number of interacting particles obey universal laws that are independent of the microscopic details. This progress was mainly due to the development of scaling theory. Since economic systems also consist of a large number of interacting units, it is plausible that scaling theory can be applied to economics. To test this possibility we study the dynamics of firm size. This may help to build a more complete characterization of the nature and processes behind firm growth. To date, the study of firm dynamics has primarily focused on whether small firms on average have higher growth rates than large firms. To a lesser extent, attention has been placed on the relationship between firm size and variation in growth rate. Our research goes beyond these questions by looking at the relationship between numerous firm characteristics and the entire distribution of growth rates. Thus, it may provide a better understanding of the mechanisms behind firm dynamics. In contrast to previous studies, this research analyzes data over many time scales, instead of just a single time interval. From a scientific standpoint, this work could be useful because it will affect the formulation of firm modeling—one of the basic building blocks of all economic analysis. In addition, this work will have practical applications. For example, there are Federal policies that are designed to encourage small businesses. While such policies might be justified on grounds other than their contribution to growth, any systematic difference in the growth rates of small and large firms might be relevant for evaluating such policies. Also, there has traditionally been a concern that an excessive amount of economic activity might become concentrated in a small number of firms. A more detailed understanding of the firm growth process will provide evidence for whether such concerns have any scientific foundation.

Scaling and universality in animate and inanimate systems

We illustrate the general principle that in biophysics, econophysics and possibly even city growth, the conceptual framework provided by scaling and universality may be of use in making sense of complex statistical data. Specifically, we discuss recent work on DNA sequences, heartbeat intervals, avalanche-like lung inflation, urban growth, and company growth. Although our main focus is on data, we also discuss statistical mechanical models.